Self-interaction Corrected Density Functional Theory Research Articles

Hyperfine interactions for small systems including transition-metal elements using self-interaction corrected density-functional theory

The interactions between the electronic magnetic moment and the nuclear spin moment, i.e., magnetic hyperfine (HF) interactions, play an important role in understanding electronic properties of magnetic systems and in realizing platforms for quantum information science applications. We investigate the HF interactions for atomic systems and small molecules, including Ti or Mn, by using Fermi–Löwdin orbital (FLO) based self-interaction corrected (SIC) density-functional theory. We calculate the Fermi contact (FC) and spin-dipole terms for the systems within the local density approximation (LDA) in the FLO-SIC method and compare them with the corresponding values without SIC within the LDA and generalized-gradient approximation (GGA), as well as experimental data. For the moderately heavy atomic systems (atomic number Z ≤ 25), we find that the mean absolute error of the FLO-SIC FC term is about 27 MHz (percentage error is 6.4%), while that of the LDA and GGA results is almost double that. Therefore, in this case, the FLO-SIC results are in better agreement with the experimental data. For the non-transition-metal molecules, the FLO-SIC FC term has the mean absolute error of 68 MHz, which is comparable to both the LDA and GGA results without SIC. For the seven transition-metal-based molecules, the FLO-SIC mean absolute error is 59 MHz, whereas the corresponding LDA and GGA errors are 101 and 82 MHz, respectively. Therefore, for the transition-metal-based molecules, the FLO-SIC FC term agrees better with experiment than the LDA and GGA results. We observe that the FC term from the FLO-SIC calculation is not necessarily larger than that from the LDA or GGA for all the considered systems due to the core spin polarization, in contrast to the expectation that SIC would increase the spin density near atomic nuclei, leading to larger FC terms.

Systematically Improvable Generalization of Self-Interaction Corrected Density Functional Theory.

Perdew-Zunger self-interaction correction (PZSIC) reintroduces an exact constraint to approximate density functional theory (DFT). However, PZSIC can paradoxically degrade performance, and standard DFT approximations (with or without PZSIC) are not systematically improvable. We use the adiabatic projection formalism (Janesko, B. G. J. Chem. Phys. 2022, 156, 014111, https://doi.org/10.1063/5.0076144) to derive PZSIC in terms of a reference system experiencing only electron self-interaction. Generalization to a "self-and-some-others" interaction introduces correlation into the reference system, systematically bridging from PZSIC to exact wave function theory without the double counting of correlation. Minimal active spaces accurately treat nearly one electron, near-equilibrium, and strongly correlated model systems at modest computational expense.

Density-related properties from self-interaction corrected density functional theory calculations.

The Perdew-Zunger self-interaction correction (PZ-SIC) removes unphysical electron self-interaction from calculations employing standard density functional approximations. Doing so improves many computed properties, bringing them into better agreement with experimental observations or with results from high-level quantum chemistry calculations. However, while PZ-SIC generally corrects in the right direction relative to the corresponding reference values, in many cases, it over-corrects. For this reason, scaled-down versions of PZ-SIC have been proposed and investigated. These approaches have mostly employed exterior scaling in which SIC correction terms are scaled in the same way at every point in space. Recently, a new local, or interior, scaling SIC method was proposed on non-empirical grounds to restore a property of the exact, but unknown, density functional that is broken in PZ-SIC. In this approach, the scaling at each point depends on the character of the charge density at that point. However, the local scaling can be done in various ways while still restoring the behavior of the exact functional. In this work, we compare and contrast the performance of various interior scaling approaches for addressing over-corrections of calculated molecular dipole moments and atomic polarizabilities and properties that reflect the nature of the electronic charge density.

Application of Self-Interaction Corrected Density Functional Theory to Early, Middle, and Late Transition States.

Density functional theory (DFT)-based methods often significantly underpredict chemical reaction barriers compared with experiments because of the tendency of DFT to overstabilize transition states with stretched bonds due to the impact of unphysical electron self-interaction. However, many reactions have early or late transition states where the transition state geometry closely resembles the reactants or products, respectively. The role of self-interaction in those cases is not known. Here we compare the performance of DFT with and without self-interaction correction (SIC) for describing the hydrogenation of CO and CO2 catalyzed by a Lewis acid-base pair incorporated onto an aromatic cluster, using CCSD(T) results for reference. The three elementary steps in these reactions consist of an early, a middle, and a late transition. Our results show that the Perdew-Zunger SIC (PZ-SIC), implemented in the Fermi-Löwdin orbital SIC (FLO-SIC) approach, qualitatively improves the description of the forward and reverse reaction barriers relative to uncorrected DFT for the middle transition but not the early or late transitions. By contrast, the local scaling SIC (LSIC) method, also implemented in the FLO-SIC framework, significantly improves the calculated barriers over DFT and PZ-SIC in all but one case. The results also show how the FLO-SIC approach can provide insight into the bonding in aromatic systems.

Symmetry Breaking within Fermi–Löwdin Orbital Self-Interaction Corrected Density Functional Theory

Fermi-Löwdin orbital self-interaction corrected density functional theory (FLO-SIC DFT) is applied to C3H5, NO3-, O3, and CH3. In general our results indicate that FLO-SIC does favor symmetric setups for molecules with nontrivial chemical bonding. Further we discuss two types of possible symmetry breaking. In the case of O3 a ground state density that breaks symmetry can be found for the symmetric molecular geometry that may be caused by insufficient treatment of correlation energy. The CH3 radical presents a second type of symmetry breaking were the lowest energy geometry becomes distorted. The latter highlights the importance of further development of approximate DFT functionals as well as further extensions of the FLO-SIC method to overcome such nonphysical artifacts.

Self-consistent self-interaction corrected density functional theory calculations for atoms using Fermi-Löwdin orbitals: Optimized Fermi-orbital descriptors for Li-Kr.

In the Fermi-Löwdin orbital method for implementing self-interaction corrections (FLO-SIC) in density functional theory (DFT), the local orbitals used to make the corrections are generated in a unitary-invariant scheme via the choice of the Fermi orbital descriptors (FODs). These are M positions in 3-d space (for an M-electron system) that can be loosely thought of as classical electron positions. The orbitals that minimize the DFT energy including the SIC are obtained by finding optimal positions for the FODs. In this paper, we present optimized FODs for the atoms from Li-Kr obtained using an unbiased search method and self-consistent FLO-SIC calculations. The FOD arrangements display a clear shell structure that reflects the principal quantum numbers of the orbitals. We describe trends in the FOD arrangements as a function of atomic number. FLO-SIC total energies for the atoms are presented and are shown to be in close agreement with the results of previous SIC calculations that imposed explicit constraints to determine the optimal local orbitals, suggesting that FLO-SIC yields the same solutions for atoms as these computationally demanding earlier methods, without invoking the constraints.

Quantum Transport Through Tunable Molecular Diodes

Employing self-interaction corrected density functional theory combined with the non-equilibrium Green’s function method, we study the quantum transport through molecules with different numbers of phenyl (donor) and pyrimidinyl (acceptor) rings in order to evaluate the effects of the molecular composition on the transport properties. Excellent agreement with the results of recent experiments addressing the rectification behavior of molecular junctions is obtained, which demonstrates the potential of quantum transport simulations for designing high performance junctions by tuning the molecular specifications.

Complex Orbitals, Multiple Local Minima, and Symmetry Breaking in Perdew-Zunger Self-Interaction Corrected Density Functional Theory Calculations.

Implentation of seminumerical stability analysis for calculations using the Perdew-Zunger self-interaction correction is described. It is shown that real-valued solutions of the Perdew-Zunger equations for gas phase atoms are unstable with respect to imaginary orbital rotations, confirming that a proper implementation of the correction requires complex-valued orbitals. The orbital density dependence of the self-interaction corrected functional is found to lead to multiple local minima in the case of the acrylic acid, H6, and benzene molecules. In the case of benzene, symmetry breaking that results in incorrect ground state geometry is found to occur, erroneously leading to alternating bond lengths in the molecule.

In2O3 Doped with Hydrogen: Electronic Structure and Optical Properties from the Pseudopotential Self-Interaction Corrected Density Functional Theory and the Random Phase Approximation

We discuss the applicability of the pseudopotential-like self-interaction correction (pSIC) to the study of defect energetics and electronic structure of In2O3. Our results predict that substitutional (at oxygen sites) and interstitial (at antibonding positions) hydrogen, as well as oxygen vacancies with charges +1 and +2, are stable configurations of defects in cubic In2O3; the former form shallow levels (only as substitutional defects), whereas the latter form deep levels. The band structure calculated with the pSIC shows an excellent agreement with experimental data. In particular, the gap for defect-free In2O3 is 2.85 eV, which compares fairly with the experimental range 2.3-2.9 eV. The pSIC results also point to a change from indirect to direct gaps depending on doping. In relation to the optical properties, obtained within the random phase approximation, it is shown that they are mostly affected by the presence of oxygen vacancies.

Quantum Monte Carlo analysis of a charge ordered insulating antiferromagnet: the Ti4O7 Magnéli phase.

The Magnéli phase Ti4O7 is an important transition metal oxide with a wide range of applications because of its interplay between charge, spin, and lattice degrees of freedom. At low temperatures, it has non-trivial magnetic states very close in energy, driven by electronic exchange and correlation interactions. We have examined three low-lying states, one ferromagnetic and two antiferromagnetic, and calculated their energies as well as Ti spin moment distributions using highly accurate quantum Monte Carlo methods. We compare our results to those obtained from density functional theory-based methods that include approximate corrections for exchange and correlation. Our results confirm the nature of the states and their ordering in energy, as compared with density-functional theory methods. However, the energy differences and spin distributions differ. A detailed analysis suggests that non-local exchange-correlation functionals, in addition to other approximations such as LDA+U to account for correlations, are needed to simultaneously obtain better estimates for spin moments, distributions, energy differences and energy gaps.

Mechanism of H2O-Induced Conductance Changes in AuCl4-Functionalized CNTs

We employ ab initio self-interaction corrected density functional theory combined with the nonequilibrium Green’s function method to study the electronic and quantum transport properties of carbon nanotubes (CNTs) functionalized with AuCl4 molecules. In particular, we investigate the electronic structure and characterize the conductance for different concentrations and configurations of randomly distributed AuCl4 molecules with and without the adsorption of H2O. We thus propose a mechanism that explains the origin of the recently observed resistivity changes of AuCl4-functionalized CNTs upon H2O adsorption. We find that water adsorption shifts the highest occupied Cl and Au states down in energy and thereby reduces the scattering of the electrons around the Fermi energy, hence enhancing the conductivity. Our results help in the development of highly sensitive nanoscale H2O vapor sensors based on AuCl4-functionalized CNTs.

Ultrafast structural pathway of charge transfer in n,n,n',n'-tetramethylethylenediamine.

We have explored the ultrafast molecular structural dynamics associated with charge transfer in N,N,N',N'-tetramethylethylenediamine using Rydberg fingerprint spectroscopy in conjunction with self-interaction corrected density functional theory. Excitation at 239 nm prepares the molecule in the Franck-Condon region of the 3s state with the charge localized on one of the two amine groups. As seen from the time-dependent Rydberg electron binding energies, the pathway of the rapidly ensuing dynamics leads through several structurally distinct conformers with various degrees of charge localization before reaching the fully charge-delocalized structure on a picosecond time scale. At several steps along the reaction path, the transient structures are identified through a comparison of the spectroscopically observed binding energies with computed values. The molecular structure is seen to evolve dynamically from an initially folded conformer to the stretched form that supports charge delocalization before an equilibrium sets in with forward and backward time constants of 1.19 (0.14) and 2.61 (0.31) ps, respectively. A coherent wavepacket motion in the charge-localized state with a period of 270 (17) fs and damping of 430 (260) fs is observed and tentatively assigned to the nitrogen umbrella motion. The damping time constant indicates the rate of the energy flow into other vibrations that are not activated by the optical excitation.

Towards an Optimal Gradient-dependent Energy Functional of the PZ-SIC Form

Results of Perdew–Zunger self-interaction corrected (PZ-SIC) density functional theory calculations of the atomization energy of 35 molecules are compared to those of high-level quantum chemistry calculations. While the PBE functional, which is commonly used in calculations of condensed matter, is known to predict on average too high atomization energy (overbinding of the molecules), the application of PZ-SIC gives a large overcorrection and leads to significant underestimation of the atomization energy. The exchange enhancement factor that is optimal for the generalized gradient approximation within the Kohn-Sham (KS) approach may not be optimal for the self-interaction corrected functional. The PBEsol functional, where the exchange enhancement factor was optimized for solids, gives poor results for molecules in KS but turns out to work better than PBE in PZ-SIC calculations. The exchange enhancement is weaker in PBEsol and the functional is closer to the local density approximation. Furthermore, the drop in the exchange enhancement factor for increasing reduced gradient in the PW91 functional gives more accurate results than the plateaued enhancement in the PBE functional. A step towards an optimal exchange enhancement factor for a gradient dependent functional of the PZ-SIC form is taken by constructing an exchange enhancement factor that mimics PBEsol formore » small values of the reduced gradient, and PW91 for large values. The average atomization energy is then in closer agreement with the high-level quantum chemistry calculations, but the variance is still large, the F2 molecule being a notable outlier.« less

Fermi orbital derivatives in self-interaction corrected density functional theory: Applications to closed shell atoms.

A recent modification of the Perdew-Zunger self-interaction-correction to the density-functional formalism has provided a framework for explicitly restoring unitary invariance to the expression for the total energy. The formalism depends upon construction of Löwdin orthonormalized Fermi-orbitals which parametrically depend on variational quasi-classical electronic positions. Derivatives of these quasi-classical electronic positions, required for efficient minimization of the self-interaction corrected energy, are derived and tested, here, on atoms. Total energies and ionization energies in closed-shell singlet atoms, where correlation is less important, using the Perdew-Wang 1992 Local Density Approximation (PW92) functional, are in good agreement with experiment and non-relativistic quantum-Monte-Carlo results albeit slightly too low.

Origin of the p-Type Character of AuCl3 Functionalized Carbon Nanotubes

The microscopic origin of the p-type character of AuCl3 functionalized carbon nanotubes (CNTs) is investigated using first-principles self-interaction corrected density functional theory (DFT). Recent DFT calculations suggest that the p-type character of AuCl3 functionalized CNTs is due to the Cl atoms adsorbed on the CNTs. We test this hypothesis and show that adsorbed Cl atoms only lead to a p-type character for very specific concentrations and arrangements of the Cl atoms, which furthermore are not the lowest energy configurations. We therefore investigate alternative mechanisms and conclude that the p-type character is due to the adsorption of AuCl4 molecules. The unraveling of the exact nature of the p-doping adsorbates is a key step for further development of AuCl3 functionalized CNTs in water sensor applications.

Ab initiostudy of electron transport in dry poly(G)-poly(C)A-DNA strands

The bias-dependent transport properties of short poly(G)-poly(C) A-DNA strands attached to Au electrodes are investigated with first principles electronic transport methods. By using the non- equilibrium Green's function approach combined with self-interaction corrected density functional theory, we calculate the fully self-consistent coherent I-V curve of various double-strand polymeric DNA fragments. We show that electronic wave-function localization, induced either by the native electrical dipole and/or by the electrostatic disorder originating from the first few water solvation layers, drastically suppresses the magnitude of the elastic conductance of A-DNA oligonucleotides. We then argue that electron transport through DNA is the result of sequence-specific short-range tunneling across a few bases combined with general diffusive/inelastic processes.

Finite-bias electronic transport of molecules in a water solution

The effects of water wetting conditions on the transport properties of molecular nano-junctions are investigated theoretically by using a combination of classical molecular dynamics and first principles electronic transport calculations. These are at the level of the non-equilibrium Green's function method implemented for self-interaction corrected density functional theory. We find that water effectively produces electrostatic gating to the molecular junction, with a gating potential determined by the time-averaged water dipole field. Such a field is large for the polar benzene-dithiol molecule, resulting in a transmission spectrum shifted by about 0.6 eV with respect to that of the dry junction. The situation is drastically different for carbon nanotubes (CNTs). In fact, because of their hydro-phobic nature the gating is almost negligible, so that the average transmission spectrum of wet Au/CNT/Au junctions is essentially the same as that in dry conditions. This suggests that CNTs can be used as molecular interconnects also in water-wet situations, for instance as tips for scanning tunnel microscopy in solution or in biological sensors.

Electron doping and magnetic moment formation in N- and C-doped MgO

The formation of the magnetic moment in C- and N-doped MgO is the result of a delicate interplay between Hund’s coupling, hybridization, and Jahn–Teller distortion. The balance depends on a number of environmental variables including electron doping. We investigate such a dependence by self-interaction corrected density functional theory and we find that the moment formation is robust with respect to electron doping. In contrast, the local symmetry around the dopant is more fragile and different geometries can be stabilized. Crucially the magnetic moment is always extremely localized, making any carrier mediated picture of magnetism in d0 magnets unlikely.

Core electron chemical shifts of hydrogen-bonded structures

We examine the possibility to study hydrogen-bonded structures through core ionization energies. We use a recently derived self-interaction corrected density functional theory method where the core ionization energies for all chemically shifted elements are obtained by a single calculation of the ground state of the structures. A direct dependency between the hydrogen atom to acceptor atom bond length and the chemical shift of the core ionization energy of the acceptor atom is found, something that has ramifications for the possibility of effective predictions of hydrogen bond lengths in hydrogen-bonded systems. This observation is verified by the conventional, much more time-consuming, self-consistent field calculations based on density functional theory.

Self-Interaction Corrected Density Functional Theory for the Study of Intramolecular Electron Transfer Dynamics in Radical Carbocations

We derived an orbital dependent Kohn-Sham based scheme for the correction of the self-interaction error in DFT, which is particularly suited for the study of open shell molecular systems. Our approach is based on a weighted form of the Perdew and Zunger (PZ) self-interaction correction scheme, in which an empirical coefficient is introduced in front of the SIC term to remove overcorrections. The method is used to investigate the first principle molecular dynamics of the intramolecular electron transfer (IET) in bis(methylene) adamanthyl radical cation and allows the analysis of the free energy surface that governs the IET process at room temperature (300 K). Indeed, the thermal activation of all molecular degrees of freedom provides important additional information about the mechanisms involved in the IET process. Our study confirms and extends previous results obtained with CASSCF and shows that there is no predominant degeneracy-lifting mode even at room temperature. However, we also identified regions in the phase space for which there is a significant probability for a productive IET event. In addition, we performed thermodynamic integrations along selected reaction coordinates to determine an estimate of the activation free energy barrier for the IET process.